Question

Solve the following questions with clear explanations...

Points: 25 ☺

Answer 1

12. For roots to be equal D = 0

b² - 4ac = 0
Here in the equation kx² - 10x + 5 = 0,
a = k
b = -10
c = 5
Putting their values
-10² - 4 x k x 5 = 0
100 - 20k = 0
20k = 100
k = 5

So required value of k = 5

13.For roots to be real D > 0
Here a = 3
b = -p
c = 3

b² - 4ac > 0
-p² - 4 x 3 x 3 >0
p² - 36 > 0
p² > 36
p > + 6 or - 6

But its given p > 0
So, p > 6 .

14.Let the side of 1 square be 'x' m
Perimeter = 4x
Perimeter of other square =  4x - 24
Side of the other square = 4x - 24 / 4 = x - 6 m

Now A/Q
x² + [x - 6]² = 468
x² + 36 + x² - 12x = 468
2x² -12x - 432 = 0
x² - 6x - 216 = 0
x² - 18x + 12x - 216 = 0
x [ x - 18] + 12[ x - 18] = 0
[x - 18][x + 12] = 0

x = 18 or x = -12

But length can't be negative.

So length of side of one square = 18 cm
other square = 18 - 6 = 12cm

15.Let the speed be x

then time taken =360/x

 When speed is increased by 5 km/h
 New speed = (x+5)km/h
Time taken = 360 / (x+5) km/h

Now A/Q --
360/x - 360/(x+5) = 1

360(x + 5)-360x /x(x+5) = 1
360x + 1800 - 360x= x(x+5)
x² + 5x = 1800
x² + 5x - 1800=0
x² + 45x - 40x - 1800=0
x(x + 45) - 40(x + 45)=0
(x - 40)(x + 45)=0

So x = 40 km/h or x = -45 km/h

But speed can't be negative.

So speed of train = 40 km/h

Hope This Helps You

Answer 2

12. For roots to be equal D = 0

b² - 4ac = 0

Here in the equation kx² - 10x + 5 = 0,

a = k

b = -10

c = 5

Putting their values

-10² - 4 x k x 5 = 0

100 - 20k = 0

20k = 100

k = 5

So required value of k = 5

13.For roots to be real D > 0

Here a = 3

b = -p

c = 3

b² - 4ac > 0

-p² - 4 x 3 x 3 >0

p² - 36 > 0

p² > 36

p > + 6 or - 6

But its given p > 0

So, p > 6 .

14.Let the side of 1 square be 'x' m

Perimeter = 4x

Perimeter of other square =  4x - 24

Side of the other square = 4x - 24 / 4 = x - 6 m

Now A/Q

x² + [x - 6]² = 468

x² + 36 + x² - 12x = 468

2x² -12x - 432 = 0

x² - 6x - 216 = 0

x² - 18x + 12x - 216 = 0

x [ x - 18] + 12[ x - 18] = 0

[x - 18][x + 12] = 0

x = 18 or x = -12

But length can't be negative.

So length of side of one square = 18 cm

other square = 18 - 6 = 12cm

15.Let the speed be x

then time taken =360/x

 When speed is increased by 5 km/h

 New speed = (x+5)km/h

Time taken = 360 / (x+5) km/h

Now A/Q --

360/x - 360/(x+5) = 1

360(x + 5)-360x /x(x+5) = 1

360x + 1800 - 360x= x(x+5)

x² + 5x = 1800

x² + 5x - 1800=0

x² + 45x - 40x - 1800=0

x(x + 45) - 40(x + 45)=0

(x - 40)(x + 45)=0

So x = 40 km/h or x = -45 km/h

But speed can't be negative.

So speed of train = 40 km/h

Hope This Helps You